Inspired by the biological and artificial systems, the nonreciprocal XY model with a vision cone interaction has been introduced.
In this talk, we clarify that the model on the square lattice with the vision cone angle in a narrow regime 
close to the standard XY model, undergoes two Kosterlitz-Thouless phase transitions,
while exhibits a single second-order phase transition for the vision cone angle outside the narrow regime.
With the short-time dynamic approach, the phase transition temperatures and critical exponents are accurately determined
for both the second-order phase transition and two Kosterlitz-Thouless phase transitions.

critical dynamics,active matter,nonreciprocal interaction